Study of the axial density/impedance gradient composite long rod hypervelocity penetration into a four-layer Q345 target

N Feng , Kun M , Chunlin Chen , Lixin Yin , Mingrui Li , Zhihu Nie ,Gng Zhou ,*, Chengwen Tn ,**

a School of Materials Science and Engineering, Beijing Institute of Technology, Beijing,100081, PR China

b Laboratory of Intense Dynamic Loading and Effect, Northwest Institute of Nuclear Technology, Xi'an, Shaanxi 710024, PR China

Keywords:Hypervelocity Density/impedance gradient Axial composite rod Penetration mechanism

ABSTRACT Based on the dynamic shock response of the material and structure,the hypervelocity impact processes and mechanisms of long composite rods with axial density/impedance gradients penetration into fourlayer targets were studied through experiments and numerical simulation methods.The propagation law of the shock waves, together with the structural responses of the projectiles and targets, the formation and evolution of the fragment groups formed during the processes and their distributions were described.The damage of each target plate was quantitatively analysed by comparing the results of the experiment and numerical simulation.The results showed that the axial density/impedance gradient projectiles could decrease the impact pressure to a certain extent,and the degree of damage to the target plate decreased layer by layer when the head density/impedance of the projectile was high.When the head density/impedance of the projectile was low, the degree of target damage first increased layer by layer until the projectile was completely eroded and then it decreased.The results can provide a reference for the design and application of long rods with axial composite structure for velocities ranging from 6 to 10 Ma or greater.

1.Introduction

Hypervelocity has become one of the leading technologies for weapons because of its characteristics, such as ultrahigh kinetic energy, superpenetration and precision-strike ability [1-3].Long rods are important kinetic energy strike weapons.The main parameters affecting the damage performance are speed, material and structure [4].In terms of speed, the launch capacity of the missile launcher limits the speed of the projectile,which is difficult to improve further,and the projectile cannot withstand the impact overload at a higher speed.For materials,the higher the density and strength of the projectile are,the larger the cross-sectional specific kinetic energy and the limitation of the length-diameter ratio of the projectile.In the past,researchers were more concerned about the penetration ability of homogeneous rods and achieved many results in experiments and theoretical models[5-9].Currently,the commonly used materials for long rods are tungsten alloy and steel,but their density and strength are relatively high and impossible to improve further.Meanwhile,due to the low strength of the junction phase,insufficient toughness and poor adiabatic shear sensitivity of the tungsten alloy, large plastic flow usually occurred, and a large mushroom-like head was formed,which resulted in an increase of resistance[10].The projectiles were prone to be unstable,and they eroded,broke and ruptured because of accumulated damage under multifrequency impact and unloading when impacting a multilayer metallic target.For structures,increasing the length-diameter ratio beyond the limitation of the materials would cause a series of problems, such as structural instability [6].To enhance the penetration performance, researchers have proposed many improved structural schemes, including segmented rods [11-16] and tuberod extended penetrators [17,18].All these structures are based on homogeneous materials to improve the penetration ability for thick metal targets or concrete targets.However, it is difficult to connect, launch or expand these projectiles because of their large length, which restricts their practical application.

It is possible to solve these problems by replacing homogeneous materials with impedance gradient composite structures and materials.This approach can make use of the gradient and multiple functions of composite structures and take advantage of the strength, hardness and dynamic failure characteristics of different materials.Currently, most research on impedance gradient structures is conducted in the areas of structures for protection from space debris and ships [19,20] or the development of impedance gradient flaps in the field of dynamic high-pressure loading [21].However, the mechanisms used in these two fields differ greatly from those of composite projectiles with large length-diameter ratios.

At present, most composite projectiles are composed of two layers(the interior and exterior parts)[22-29]or two sections(the front and back parts) [30-32].For axial composite projectiles, Wu et al.[30] designed a post-composited rod, and its maximum penetration depth was 25% greater than that of a homogeneous tungsten rod at a velocity of 3.5 Ma.It took advantage of the high density of tungsten during the early stage at high penetration speed and the good abilities of tungsten carbide to resist deformation and erosion in the later stage at low penetration speed.Hu et al.[31]proposed a multilayer composite warhead and analysed the influence of different material combinations on the residual kinetic energy and ballistic stability of the projectile.The performances of two-layer and three-layer warheads are better than those of homogeneous projectile,which can provide a reference for the design of warheads.Tang et al.[32]designed an axial heterogeneous long rod composed of 5 layers of materials(40CrNiMoA steel,Q490 steel,Q490 steel, Q235 steel and Q235 steel) with material strength decreasing from the head to the tail.The penetration performance was significantly better compared with that of the Q235 homogeneous rod.However,most composite projectiles were designed for thick targets, while the design and application of axial composite projectiles for multilayer metallic targets are limited.

The penetration of a long rod projectile into a multilayer target is a highly nonlinear and complex problem.To describe the dynamic process, it is necessary to consider the work hardening behaviour, strain rate effect, elastoplastic deformation, impact phase transition,rupture,damage,shock wave propagation and so on [33].The amplitudes of the reflected tension wave and the unloading wave are very closely related to the gradient distribution of the composition.The distributions of the equivalent plastic strain, kinetic and elastic strain energies are dependent on the gradient distribution of the composition.Because of the limitations of technologies and methods, there are few experimental data for the hypervelocity impact of rod projectiles on multilayer targets under 6-10 Ma.Most of the research studies use theoretical models[34]and numerical simulations[35].In summary,there is an urgent need to analyse the shock wave propagation characteristics of rod projectiles with different impedance distributions, to clarify the damage processes and failure modes of projectiles/targets and to optimize the impedance structure of projectiles to realize strong destruction.

In this study, the hypervelocity impact processes and mechanisms of the penetration of novel long composite rods with axial density/impedance gradients into four-layer targets were studied.The propagation law of the shock waves, together with the structural responses of the projectiles and targets, the formation and evolution mechanisms of the fragment groups formed during the process and their distributions were first described in detail.The damage to the target plates was quantitatively analysed by comparing the results of the experiment and numerical simulation.

2.Axial density/impedance gradient rod projectile

2.1.Mechanical properties of materials under hypervelocity impact

According to the shock wave conservation equations,the initial mechanical parameters of different materials under hypervelocity impact were calculated, and the wave impedance characteristics and penetration abilities of different materials were analysed.The results can provide theoretical support for the subsequent design of projectiles with density/impedance gradients.

When the rod projectile impacts the target at hypervelocity v0,it produces extremely high pressure at the target interface in the form of a shock wave.The shock wave continues to propagate into the projectile (shock wave S1) and the target interior (shock wave S2).At the contact surface of the target and projectile,the pressure and particle velocity of the target and projectile after the shock wave are equal.According to the mass and momentum conservations, the relationships can be presented as follows:

The initial shock wave pressure is p1, and the densities of the projectile before and after the shock wave are ρp0and ρp1,respectively.The densities of the target before and after the shock wave are ρt0and ρt1, respectively.The shock wave velocities of S1and S2are U1and U2,respectively.The particle velocities of the projectile before and after the shock wave are v0and v1, respectively.The particle velocities of the target before and after the shock wave are 0 and v1,respectively.

In addition, the relationship between the shock wave velocity and particle velocity is as follows:

where c0and s are Hugoniot parameters of the materials.By solving these equations through a numerical method, the initial shock wave parameters of different materials can be obtained.Materials suitable for composite projectiles can be selected according to these parameters.

Table 1 shows the initial shock wave parameters of different materials impacting the Q345 plate at a velocity of 2.3 km/s.The impact impedance and the elastic impedance are defined as the product of ρ*U and ρ*c0, respectively.

2.2.Materials selection

Some materials have a higher impact impedance but a lower elastic impedance relative to the adjacent material in Table 1,such as Cu.When the strength of the impact shock increases,the impact impedance of these materials may first be lower and then higher than those of the adjacent materials.To maintain the consistency of the distributions of impact impedance and density,these materials were excluded from this study.Moreover,the dynamic behaviour of the materials would not be consistent when their strength was too high or too low; thus, materials such as Pb were excluded.

Table 1Dynamic parameters of different materials impacting a Q345 plate at a velocity of 2.3 km/s.

The structure with three sections composed of three materials was selected to meet the requirements of processing and to conduct the experiment.For a kinetic energy projectile, there is a strong correlation between the damage ability and the density of the material, and the most important factor to consider when choosing materials is that the density of the material is high.In this study, 93 W with high density and steel as the commonly used material for long rods were chosen.The aluminium alloy has the least impact impedance, the fastest shock wave velocity and the greatest unloading capacity among the materials listed in Table 1.The ability of the aluminium alloy to damage and penetrate Q345 target is relatively low due to its low density.Compared with the aluminium alloy, the density of the titanium alloy (TC4) is 60%higher, and the wave impedance is 50% larger, although the shock wave velocity is 5%slower.Finally,three materials,93 W Q345 and TC4, were chosen, and an axial density/impedance gradient could be formed in the composite rod.

3.Numerical simulations

3.1.Description of the simulation model

To gain insights into the damage mechanism and the penetration process, three-dimensional numerical simulations were performed by the smooth particle hydrodynamics(SPH)method using the AUTODYN finite element code.The projectile was a long rod with a diameter of 12 mm and a length of 40 mm consisting of 93 W Q345 and TC4 in turn or in reverse order.The targets were round Q345 plates with a thickness of 4 mm.The diameters of the first layer and the latter layers were 80 mm and 100 mm, respectively.The distance between each two plates was 179 mm.As the model was axisymmetric, a 1/2 model (Fig.1) was established to save calculation time.The smooth length was 0.4 mm, which had been compared and validated, and both the result error and calculation time consumption were acceptable.

Fig.1.Simulation model of a composite projectile impacting a four-layer target.

3.2.Material models

An overview of the material models is shown in Table 2.

The GRAY two-phase equation of states written by the userdefined program module was used to describe the equations of state.The equation can provide the relation of pressure,volume and internal energy in both solid and liquid phases.The GRAY twophase equation describes the solid-liquid phase region based on Grover's liquid metal calibration law equation[36].The phase state is classified into the solid phase, molten phase, liquid phase and thermal liquid phase by the initial melting energy Em1,total melting energy Em2and constant specific heat energy EGG.The phase state can be evaluated according to the value of the internal energy E;Then,the correction pressure pcand temperature of the material T can be obtained by the expressions as follows:

When E ≤Em1,

where x=1-V/V0is the specific volume, E0is the cold energy,and G′, R′,γe,γ0and a are all material parameters.

When Em1

where Tmis the melting temperature of the material, δT is the change in temperature,and ν =（E -Em1）/（Em2-Em1）,ΔS′,and α′are material parameters.

When Em2≤E ≤EGG,

where λ is the parameter correlation to the Grüneisen coefficient.

When E>EGG,

where Γ is the material parameter.

Based on the above equations, the actual pressure p of the material can be obtained by combining the linear Grüneisen pressure p1with the modified pressure terms pcand pcc.The relationships are as follows:

Table 2Material models.

where T0is the initial temperature and c0,s,and γ0are the impact Hugoniot parameters of the materials.

The parameters are shown in Table 3.As the pressure expression of the GRAY two-phase state equation in the solid phase is consistent with that of the Mie-Grüneisen state equation,the solid phase material parameter of the GRAY two-phase state equation is the same as that of the Mie-Grüneisen state equation.Other material parameters are provided by Royce [36].The accuracy of the expressions and parameter selection has been verified and discussed [35].

The Johnson-Cook(J-C)model,which is capable to represent the constitutive response of materials under large-strain, high deformation rate, and high-temperature conditions, is commonly used in models of hypervelocity impact.The yield stress,Y,is defined as

where εpis the equivalent plastic strain, ˙εpis the equivalent plastic strain rate, T is the temperature, T0is the reference temperature,and Tmis the melting temperature.The strength model parametersof 93 W Q345 and TC4 (A, B, n, c, m) are listed in Table 4.

Table 3Equations of state model parameters of 93 W Q345 and TC4.

Table 4Strength model parameters of 93 W Q345 and TC4.

Table 5Failure model parameters of 93 W Q345 and TC4.

To accurately calculate the erosion and destruction of the target during the impact process,the J-C failure model which considered the stress triaxiality strain rate and temperature effect was applied.The fracture failure strain of the material is expressed as follows:

where D1-D5are material parameters.σ*=-p/σeqis the stress triaxiality, and σeqis the equivalent stress.

The J-C failure model assumes that damage accumulates when the material undergoes plastic deformation.By using the damage variable, the damage evolution of the element can be defined as

where Δεeqis the equivalent plastic strain increment at each step of damage accumulation.Its initial value is 0, the strength of the material is unchanged when the damage develops, and when it

Fig.2.Structure of the axial density/impedance gradient projectile and the sabot.

reaches 1, the material fails.The material parameters of the J-C failure model are shown in Table 5.

3.3.Fragment identification and statistics

A user-defined subroutine was used to output the SPH particlerelated data into an external file from the simulation results.The broad priority search (BFS) algorithm was adopted to search the fragments.First, the whole SPH particle space is divided into a regular subgrid with a fixed edge length to ensure that the edge of the subgrid length is longer than the search radius.Therefore,when one subgrid is being searched,the search space can be reduced to the subgrid and its adjacent subgrids, which can greatly reduce the search time.In this study,the fragment group was considered to be fully extended at 100 μs,and 1.1 times the smooth length was used to determine whether two particles belonged to one fragment;thereby, the fragments were identified, and the characteristic parameters were obtained.On this basis,the distribution of the characteristic parameters of the fragment groups was further analysed.

4.Experimental research

All impact tests presented in this paper were performed at the Northwest Nuclear Technology Institute using a 155/65-mm, twostage, light-gas gun.The structure of the axial density/impedance gradient projectile is shown in Fig.2.The joint type was a thread connection,and all the geometric parameters of the projectile and the target were the same as the simulation model.The impact velocity was determined by the laser shielding method with laserphotodetector systems installed along the flight path of the projectile.The sabot was made of polycarbonate with a three-section type structure and forced to be separated by pneumatic separation and an impact separator.

Fig.4.(a) Positions of the gauge points and (b) and (c) the pressure of different projectiles impacting the 4 mm target plate at 2.3 km/s.

Fig.5.Pressure of different projectiles impacting the 4 mm target plate at (a) 2.0 km/s; (b) 2.3 km/s; (c) 3.0 km/s; (d) 3.4 km/s.

Table 6Decay efficiency of pressure in the middle section of projectiles when impacting the 4 mm target plate at 2.0, 2.3, 3.0 and 3.4 km/s.

5.Results and discussion

5.1.Mechanical response of the axial density/impedance gradient projectiles

Fig.3 shows the deformation and failure of different projectiles and the 4 mm target plate at 20 μs.Compared with the homogeneous Q345 projectile, the penetration ability of the composite projectile with a 93 W head (93 W-Q345-TC4) was stronger, its fragment group had higher axial and radial velocities, and the erosion of the projectile was less, which showed that the 93 WQ345-TC4 composite rod could effectively protect the integrity of the rear structure.However, the penetration ability of the composite rod with the TC4 head (TC4-Q345-93 W) was weak, and it was difficult to form fragments with high radial velocity.The TC4 head was completely eroded,and deformation and material failure were found in the middle section.

To further analyse the propagation of shock waves in different projectile structures,gauge points were set at the same positions as shown in Fig.4(a).Red,blue and green curves represent the results of the 93 W-Q345-TC4, TC4-Q345-93 W and the Q345 projectiles,respectively.The shock wave amplitude of 93 W was the highest as its impact impedance was the highest, the value of Q345 was the second highest and TC4 was the lowest.The values of shock wave velocities from high to low were TC4, Q345 and 93 W.The peak value of the points in the middle section of the Q345 projectile became the highest, and the values of the composite projectiles were smaller.This shows that regardless of the material of the front section,the impact pressure in the middle section of the projectile could be reduced to some extent.This may be attributed to the transmission and reflection of the shock wave at different material interfaces,which prevents the energy of the shock wave from being fully coupled into the middle section.Moreover, the impact stress can be propagated to the middle section more quickly if the front section is TC4.

5.1.1.Influence of the impact velocity

The peak value of pressure and pulse width of the shock wave are closely related to the impact velocity, projectile diameter and target thickness.The pressure results at gauge points in different projectiles when impacting the 4 mm target plate at 2.0 km/s, 2.3 km/s, 3.0 km/s and 3.4 km/s are shown in Fig.5.As the impact velocity increased, the pressure increased, and the pulse width became shorter.The pressure difference value in the middle section of different projectiles decreased macroscopically.When the pressure decay efficiency in the middle section of the Q345 projectile was considered to be 0%,the pressure decay efficiency in the axial density/impedance gradient projectiles was shown in Table 6.It is obvious that the buffering effect of the 93 W-Q345-TC4 projectile was stronger than that of the TC4-Q345-93 W projectile,and the value decreased as the impact velocity increased,which means that the buffering effect decreased as the velocity increased in the range of 6-10Ma.

5.1.2.Influence of target thickness

When the projectile impacted the target,the shock wave in the target was reflected to the tension wave from the back of the target(the former wave),and it continued to pursue and unload the shock wave in the projectile.The rarefaction wave formed on the lateral free surface of the projectile (the latter wave).When the target thickness was 1.5 mm,the peak value of the shock wave decreased,and the pulse width became shorter compared with the result of 4 mm, as shown in Fig.6.Even though the initial intensity of the shock wave was the same, the former wave propagated to the projectile sooner than the latter(2 times the thickness of the plate is shorter than the projectile radius), and the influence of the former wave was more significant.Moreover, tensile failure occurred in more parts of the projectile subjected to the reflection of tensile waves as the pressure returned to 0.When the target thickness was 9 mm,the results were basically the same as those of 4 mm due to the main influence of the latter wave.In addition,the blue-18 and green-30 gauge points were compressed again with peak values smaller than that of the initial shock.

Fig.6.Pressure of different projectiles impacting (a) 1.5 mm, (b) 4 mm, (c) 9 mm target plates at 2.3 km/s.

Table 7Penetration results of different projectiles impacting a 4 mm Q345 plate.

Fig.8.Distribution of fragment number vs.specific axial velocity: (a) 93 W-Q345-TC; (b) TC4-Q345-93 W; (c) Q345 projectiles.

Fig.9.Distribution of fragment mass vs.specific axial velocity: (a) 93 W-Q345-TC; (b) TC4-Q345-93 W; (c) Homogeneous Q345 projectiles.

Fig.10.Distribution of fragment axial momentum vs.specific axial velocity: (a) 93 W-Q345-TC; (b) TC4-Q345-93 W; (c) Q345 projectiles.

Fig.11.Distribution of fragment radial momentum vs.specific axial velocity: (a) 93 W-Q345-TC; (b) TC4-Q345-93 W; (c) Q345 projectiles.

5.2.Distribution of the fragment groups

Fig.7 shows the numerical simulation results of the fragment groups produced by different projectiles impacting the 4 mm target plate at 100 μs.For the 93 W-Q345-TC4 projectile, spallation occurred in the target plate, and there was a cusp in front of the fragment group.For the TC4-Q345-93 W projectile,the penetration ability was weaker, the long axis of the ellipsoid profile of the fragment group was longer, and its radial expansion velocity was lower.The penetration results of different projectiles impacting a 4 mm Q345 plate are shown in Table 7.The damage ability of the 93 W-Q345-TC projectile was basically equivalent to that of the 93 W projectile, but the weight of the axial composite projectile could be reduced by 43.3%.

Figs.8 and 9 show the distributions of fragment number and mass vs.specific axial velocity (the ratio of the axial velocity of fragment vxto the residual axial velocity of the projectile vp) produced by different projectiles.As the axial and radial velocities of the fragments were equal to the displacements in the corresponding direction, the distribution of the fragment group vs.the specific axial velocity could be regarded as the spatial distribution of the fragments.Meanwhile, fragments with different masses are represented by different colours, as shown in the legends.In general,more fragments were distributed in the front than the tail,and the distribution in the middle was the lowest.The reason was that the head of the projectile continued to undergo dynamic erosion and damage after the projectile penetrated the target plate, and fragments with large masses were easily concentrated in the front of the fragment group.For the 93 W-Q345-TC4 projectile, the penetration ability was strong because of the high density of the projectile head; even though there was little mass erosion, the distributions of fragment number and mass were much larger at the head of the fragment group than for other parts.Moreover,the 93 W-Q345-TC4 projectile head is fully broken; there were many more fragments,and fewer fragments with large mass,than for the other two projectiles.

Fig.12.Distribution of fragment number vs.specific radial distance on the 2nd target plate: (a) 93 W-Q345-TC; (b) TC4-Q345-93 W; (c) Q345 projectiles.

Fig.13.Distribution of fragment mass vs.specific radial distance on the 2nd target plate: (a) 93 W-Q345-TC; (b) TC4-Q345-93 W; (c) Q345 projectiles.

Fig.14.Distribution of fragment accumulated kinetic energy vs.specific radial distance on the 2nd target plate: (a) 93 W-Q345-TC; (b) TC4-Q345-93 W; (c) Q345 projectiles.

Fig.15.Damage of each layer of target plates impacted by the 93 W projectile at 2.09 km/s.

Figs.10 and 11 show the distributions of the axial momentum and radial momentum of the fragment groups vs.the axial specific velocity.The large axial momentum and radial momentum are normally concentrated in the front and middle of the fragment group because of the large total mass of the front and middle fragment group.The axial momentum distribution of the 93 WQ345-TC4 projectile was the most concentrated,and the results of the Q345 projectile were relatively uniform.The results showed that the higher the material density of the projectile head was,the greater the total mass of the fragment group,the mass of the front fragment group, axial momentum and radial momentum of the fragment group.In terms of damage ability, the front and middle fragment group were the most destructive.

The distributions of fragment number, mass and accumulated kinetic energy vs.specific radial distance (the ratio of radial distance of fragment drto the distance between two target plates d)on the 2nd target plate are shown in Figs.12-14, respectively.The damage ability of the fragment group to the 2nd layer was concentrated mainly in the central area and decayed exponentially along the radial direction.This would change the morphology of the damage from perforations to craters along the radial direction.The number, mass and accumulated kinetic energy of the 93 WQ345-TC projectile were the largest, while those of the TC4-Q345-93 W projectile were the smallest (only one-third of those of the 93 W-Q345-TC projectile).When the density of the projectile head was higher, the mass and kinetic energy of the fragments that impact the next layer were larger.

Fig.16.Damage of target plates impacted by the 93 W-Q345-TC projectile at 2.1 km/s.

Fig.17.Damage of target plates impacted by the TC4-Q345-93 W projectile at 2.1 km/s.

Fig.18.Damage of the 2nd-4th plates impacted by the 93 W projectile.

Fig.19.Distribution of accumulated fragment mass on the 2nd-4th plates vs.specific radial distance impacted by the 93 W projectile.

Fig.20.Distribution of the accumulated fragment kinetic energy on the 2nd-4th plates vs.the specific radial distance impacted by the 93 W projectile.

5.3.Experimental results and discussion

Fig.15 presents the damage morphologies of target plates impacted by the 93 W projectile at 2.09 km/s.Four layers of the target were penetrated.To compare the damage degree more intuitively,some concentric circles were marked on the plates.The radii of the green, yellow and red circles were 17.9 mm, 35.8 mm and 100 mm,respectively.The perforation on the first target plate showed that the failure form was central perforation.There was almost no deformation in the plate because of the high initial velocity of the projectile,and the impact pressure on the target plate was much higher than the failure strength of the target material.The diameter of the central hole was approximately 17 mm,which indicated that the projectile caused hole expansion because of dynamic shear failure and extrusion.After penetrated the first target plate, the projectile combined with the formed fragment group continued to impact the following plates.The plates deformed, bent forwards, yielded and deformed under the large tensile stresses, which resulted in the formation of microcracks.Under the impact of the fragment group,the microcracks continued to expand to cause petal deformations.Many discrete holes,craters and bulges formed on the back of the plates.As the penetration continued,the velocity and mass of the projectile decreased,and its penetration ability and the number of fragments and craters decreased layer by layer.

Fig.22.Distribution of accumulated fragment mass on the 2nd-4th plates vs.specific radial distance impacted by the 93 W-Q345-TC projectile.

Fig.23.Distribution of the accumulated fragment kinetic energy on the 2nd-4th plates vs.specific radial distance impacted by the 93 W-Q345-TC projectile.

Figs.16 and 17 show the damage of target plates impacted by the 93 W-Q345-TC and TC4-Q345-93 W projectiles at 2.10 km/s; all 4 layers of the target plates were penetrated.The damage morphologies of the first two layers impacted by the 93 W-Q345-TC4 projectile were similar to those of the 93 W projectile.From the 3rd layer on, the central hole and whole damage area were obviously reduced because the head of the projectile was completely eroded.For the TC4-Q345-93 W projectile,the damage areas of the first two layers were smaller than those of the 93 WQ345-TC4 projectile, but from the 3rd layer on, the results were equal to or even greater than those of the 93 W-Q345-TC4 projectile.The main reason for the difference was that the fragment penetration ability of 93 W at the tail of the TC4-Q345-93 W projectile was stronger.

5.4.Numerical simulation results and discussion

To quantitatively analyse the damage mechanism of different projectiles impacting multilayer targets, the results of the experiment and simulation were compared.As the difference in the 1st layer was slight,the 2nd through the 4th layers were compared and discussed herein.Fig.18 shows the damage of the experiment and the equivalent plastic strain cloud diagrams of the 2nd-4th plates penetrated by the 93 W projectile.The concentric circles were marked to show the results more intuitively.The smallest and largest circle diameters were 17.9 mm and 100 mm, respectively.The diameter difference value was 17.9 mm.The numerical simulation damage results were in good agreement with the experimental results.Figs.19 and 20 show the distribution of fragment mass and accumulated kinetic energy vs.specific radial distance on the 2nd-4th plates.Five groups of data from 0.1 to 0.5 correspond to the 5 inner circles.On the 2nd and 3rd plates, the accumulated kinetic energy was～7.8×106J and 5.1×106J within the 0.1 to 0.2 interval,and the average accumulated kinetic energy per unit area was ～2.6 kJ/mm2and 1.7 kJ/mm2, respectively.In other words,when the average kinetic energy per unit area of the fragment group was greater than 1.7 kJ/mm2, it could cause perforation damage and petal-shaped cracking damage in the plate.

Fig.21 shows the results for the experiment and the equivalent plastic strain cloud diagrams of the 2nd-4th plates penetrated by the 93 W-Q345-TC projectile.The simulation results of the 2nd and 4th plates were consistent with those of the experiment, but the result of the 3rd plate was larger.The damage of the target and the accumulated mass and the kinetic energy of the fragment decreased layer by layer.The central hole size of the 2nd layer target plate was～36 mm.The accumulated mass and kinetic energy in Figs.22 and 23 show that the maximum total accumulated kinetic energy of the fragment was ～8.2 × 106J.The accumulated mass on the 3rd plate was greater than that of the 2nd plate,but the accumulated kinetic energy decreased by 60%, which led to a smaller central perforation on the 3rd plate.Compared with the 2nd layer,the accumulated mass on the 4th layer decreased by 1/3,the accumulated kinetic energy was one order of magnitude smaller, and the damage area obviously decreased.Overall, the degree of damage decreased layer by layer, which reflected the structural characteristics of the projectile.

The experimental damage of the target plates impacted by the TC4-Q345-93 W projectile was consistent with the simulation results in Fig.24.The accumulated mass and kinetic energy on the 2nd plate in Figs.25 and 26 were obviously less than those of the 93 W-Q345-TC projectile.The accumulated mass on the 4th layer was larger than the results of the 2nd and 3rd layers,which showed that the projectile began to form tungsten fragments with large masses when it impact the 3rd layer.The accumulated kinetic energy on the 3rd layer was less than that of the 2nd layer within the 0.2 to 0.5 intervals,but it could cause more severe damage because of the high fragment density.Overall,the damage ability of the TC4-Q345-93 W projectile was considered to increase layer by layer and then decrease after the projectile was completely broken.

Fig.24.Damage of the 2nd-4th plates impacted by the TC4-Q345-93 W projectile.

Fig.25.Distribution of accumulated fragment mass on the 2nd-4th plates vs.specific radial distance impacted by the TC4-Q345-93 W projectile.

Fig.26.Distribution of the accumulated fragment kinetic energy on the 2nd-4th plates vs.specific radial distance impacted by the TC4-Q345-93 W projectile.

6.Conclusions

In this study, the process of long rods with different axial densities/impedance gradients penetration into four-layer Q345 targets was researched.The influence of density gradient sequences,impact velocities, and target thicknesses were discussed.The mechanisms of penetration were identified, and the conclusions are as follows.

(1) The shock wave was strong, and the pulse width was long,when the head density/impedance of the projectile was high,and the penetration ability of the projectile and the radial expansion velocity of the formed fragment group were strong.In contrast,the results were the opposite for low head density/impedance.

(2) The axial density/impedance gradient structure could decay the shock wave in the projectile and protect the rear of the projectile;the buffering effect of the impact decreased as the velocity increased in the range of 6-10 Ma.

(3) The axial distribution of the fragment group was large at the front and small at the tail.When the average kinetic energy per unit area of the fragment group was greater than 1.7 kJ/mm2,perforation damage and petal-shaped cracking formed.

(4) Although the weight of the axial composite projectiles was 43.3% less compared with the 93 W projectiles, the penetration abilities were basically equivalent.The damage degree of the target plate impacted by the 93 W-Q345-TC projectile decreased layer by layer.For the TC4-Q345-93 W projectile, the damage degree of the target plate was considered to increase layer by layer and then decrease after the projectile was completely broken.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China(Grant No.11772269).The authors would like to thank Pro.Suo Tao of Northwestern University of Technology and Wen Heming of China University of Science and Technology for the constitutive model parameters of the materials.